explain Euler's formula with diagram.....(•‿•)
Answers
explain Euler's formula with diagram ?
ans :- The Euler formula tells us that all plane drawings of a connected planar graph have the same number of faces namely, 2+m-n. Theorem 1 (Euler's Formula) Let G be a connected planar graph, and let n, m and f denote, respectively, the numbers of vertices, edges, and faces in a plane drawing of G. Then n - m + f = 2.
✔A triangular pyramid has 4 faces, including the base, are triangles, 4 veritces and 6 edges.
Faces = 4
Vertices = 4
Edges = 6
F + V = E + 2
F + V - E = 2
This relationship is called Euler's Formula.
⇒ 4 + 4 - 6 = 2
⇒ 8 - 6 = 2
⇒ 2 = 2
L.H.S. = R.H.S.
Hence, The Euler's Formula is verified for a Triangular Pyramid.
Answer:
explain Euler's formula with diagram ?
ans :- The Euler formula tells us that all plane drawings of a connected planar graph have the same number of faces namely, 2+m-n. Theorem 1 (Euler's Formula) Let G be a connected planar graph, and let n, m and f denote, respectively, the numbers of vertices, edges, and faces in a plane drawing of G. Then n - m + f = 2.
✔A triangular pyramid has 4 faces, including the base, are triangles, 4 veritces and 6 edges.
Faces = 4
Vertices = 4
Edges = 6
F + V = E + 2
F + V - E = 2
This relationship is called Euler's Formula.
⇒ 4 + 4 - 6 = 2
⇒ 8 - 6 = 2
⇒ 2 = 2
L.H.S. = R.H.S.
Hence, The Euler's Formula is verified for a Triangular Pyramid.